Stability of Time-Delay Systems
Stability of Time-Delay Systems
Simple stability criteria for systems with time-varying delays
Automatica (Journal of IFAC)
ACC'09 Proceedings of the 2009 conference on American Control Conference
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
Stability of linear systems with uncertain bounded time-varyingdelays is studied under the assumption that the nominal delayvalues are not equal to zero. An input-output approach to stabilityof such systems is known to be based on the bound of theL2-norm of a certain integral operator. There exists abound on this operator norm in two cases: in the case where thedelay derivative is not greater than 1 and in the case without anyconstraints on the delay derivative. In the present note we fillthe gap between the two cases by deriving a tight operator boundwhich is an increasing and continuous function of the delayderivative upper bound d≥. For d➝∞ the new boundcorresponds to the second case and improves the existing bound. Asa result, for the first time, delay-derivative-dependent frequencydomain and time domain stability criteria are derived for systemswith the delay derivative greater than 1.